#mathematical discovery

[frank-olivier]

Mathematics in the Age of Automation: Navigating the Opportunities and Challenges of AI

The convergence of Artificial Intelligence and mathematics, exemplified by the Alpha Proof project, heralds a transformative era for the field, yet its full potential remains contingent upon addressing inherent challenges. A recent conversation with key contributors provided invaluable insights into the application of AI in mathematical reasoning, proof verification, and discovery.

Alpha Proof's architectural lineage from Alpha Zero underscores the viability of Reinforcement Learning in navigating the vast mathematical search space, as evidenced by its solutions to a subset of International Mathematical Olympiad problems. However, the project's true transformative potential lies not merely in its problem-solving prowess, but in its capacity to facilitate collaborative mathematics by automating proof verification, thereby freeing human mathematicians to pursue more abstract and innovative endeavors.

A significant impediment to the widespread adoption of such AI tools is their inaccessibility to the broader mathematical community. The development of intuitive interfaces and educational resources, particularly in formal proof systems like Lean, is crucial for democratizing access to these technologies. By doing so, not only can the collaboration between humans and AI be enhanced, but also personalized learning experiences can be offered, thereby bridging the gap between computational mathematics and traditional mathematical practices.

The symbiotic relationship between human creativity and AI capabilities emerges as a pivotal theme. While AI excels in the structured realm of theorem-proving, human ingenuity remains indispensable in the more ephemeral domain of theory-building, where the selection of problems and the formulation of novel questions dictate the trajectory of mathematical progress. This dichotomy suggests a future where AI augments human capabilities, enabling a deeper exploration of mathematical truths, while humans continue to drive the creative impetus behind theoretical advancements.

Google's DeepMind's AlphaProof Team (No Priors, November 2024)

Friday, November 15, 2024

[boycritter]

had a really cool idea for an Art Thing yesterday and i drew a concept sketch for it and it also looked cool and i sent it to my friend and he said it looked cool and so basicallly im on top of the world

[rivenantiqnerd]

I love women in stem

do YOU 🫵 love women in stem??

[dearreader-12]

I've discovered two important women in STEM today!

Emmy Noether who was an outstanding mathematician who doesn't get enough credit for the work she did for the world of math and physics! She is the reason why in physics you learn that momentum is conserved for isolated systems, she discovered that!

Stephanie Kwolek who was the main inventor for Kevlar armor by finding the chemical compound that makes up the material of the armor. She also contributed to helping invent Spandex!

Imagine how many more achievements are still undiscovered to this day that could change the world as we know it. And now, women are more likely to be allowed to be involved in those discoveries! Shoot for the stars everyone, maybe you could be the one to discover something groundbreaking!

[g0fckur531f]

[atsushis-missing-leg]

Somehow... I found math fun for a couple minutes.

[manoasha]

The Genius Who Changed Everything: Isaac Newton's Journey 🍎🌌

Early Days: Isaac Newton was born on January 4, 1643, in England. He grew up on a farm, but from a young age, everyone could see he was super smart. Big Achievements: Newton did some super cool stuff with numbers and science. His most famous work, “Philosophiæ Naturalis Principia Mathematica,” taught us about how things move and why stuff falls down. Imagine understanding why an apple falls from…

[evolooka]

As Tesla said, it's all about frequency and vibration.

[xtruss]

Michigan State Students Discover Traces of School's First Observatory Built in 1881

— August 14, 2023 | Juliana Kim | NPR

The exterior of MSU's first campus observatory, circa 1900. Michigan State University Archives and Historical Collections

When Stacey Camp, an anthropology professor at Michigan State University, learned there was a hard, impenetrable surface underground north of campus, she assumed it was just a large rock.

But historic maps hinted at something bigger. After careful digging, her team of campus archeologists unearthed parts of a foundation that once belonged to the university's original observatory.

"What's exciting about this particular find is that it tells the story of how our campus and how higher education has changed so radically over time," Camp said.

The foundation of school's first observatory. The discovery gives insight into how scientific observation, as well as life on campus, has changed since the original observatory was built in 1881. Nick Schrader

The former observatory was built in 1881 by Rolla Carpenter, a former student and professor who taught a host of topics from mathematics, astronomy and French. He advocated for an observatory after the university acquired its first telescope. At the time, students would observe the sky on the roof of a campus building.

Fast forward to this past May, 142 years later. Construction workers were drilling hammock posts outside a residence hall when they hit something unusually hard beneath the ground. The crew later phoned the school's Campus Archaeology Program, tasked with investigating and preserving buried archaeological sites discovered accidentally on campus.

The program's staff cross-referenced the location with historic maps, which suggested that it was in same area of the university's first observatory.

"That could have been easily dismissed if we hadn't had some historic maps and knowledge of that area," said Camp, who is the director of the program.

A group of undergraduate and graduate students spent the next several weeks documenting, digging and excavating around the site until it became clear that the curious impenetrable surface was indeed the foundation of a previous school building.

MSU Campus Archaeology students dig up the first observatory located on Michigan State's campus, next to Wills House, June 8. Nick Schrader

On Monday, results from a ground-penetrating radar survey revealed that most of the foundation is intact. According to Camp, its condition is a "miracle" given all the changes and construction that have taken place on campus.

"You've got a sidewalk next to it. You've got a road there. You've got a dormitory, a basketball court," she said. "All of that has destroyed a lot of our historic space on campus."

The discovery was especially special for Levi Webb, a rising senior studying astrophysics and anthropology.

Webb did not know about the former observatory before he joined the archaeology project. The search left him wondering about the students who frequented the space and their shared interest in astronomy.

"Each of these people had a life just as vibrant as mine," he said. "That's all it takes, a little discovery to unearth this complete, complex history."

Individuals pose outside of the school's first observatory, circa 1888. The observatory is located behind where Willis House now stands on MSU's campus, just south of Grand River in North Neighborhood. Michigan State University Archives and Historical Collections

The project also was a boon for Webb's job at the current observatory. During a recent tour, Webb shared what his team uncovered and the differences between the old and new buildings.

"We have always talked about the history of the current observatory, which was built in 1969," he said. "But now, I can enrich that with, this has gone back even farther than 1969, all the way back to 1880."

Next summer, the program is expected to run a larger excavation project to uncover more of the foundation and possible artifacts along the way.

[floralfemmes]

was talking to my mom about how white people ignore the contributions of poc to academia and I found myself saying the words "I bet those idiots think Louis Pasteur was the first to discover germ theory"

which admittedly sounded pretentious as fuck but I'm just so angry that so few people know about the academic advancements during the golden age of Islam.

Islamic doctors were washing their hands and equipment when Europeans were still shoving dirty ass hands into bullet wounds. ancient Indians were describing tiny organisms worsening illness that could travel from person to person before Greece and Rome even started theorizing that some illnesses could be transmitted

also, not related to germ theory, but during the golden age of Islam, they developed an early version of surgery on the cornea. as in the fucking eye. and they were successful

and what have white people contributed exactly?

please go research the golden age of Islamic academia. so many of us wouldn't be alive today if not for their discoveries

people ask sometimes how I can be proud to be Muslim. this is just one of many reasons

some sources to get you started:

but keep in mind, it wasn't just science and medicine! we contributed to literature and philosophy and mathematics and political theory and more!

maybe show us some damn respect

[xcookedxchroniclesx]

Here's my basics to upwards math. It can get incredibly complex if you let it. It doesn't have algebra yet or subtraction. I think it is a more precise math because you are going upwards so all you do is add to get to your number while downwards you have to subtract from the higher definitive value down to your number. Downwards math eventually ends to, not upwards.

[fuckyeahisawthat]

So OBVIOUSLY Jayce is as smart as Viktor; I don't think Viktor would give him the time of day if he wasn't. But I think he does have a bit of the Elle Woods "What, like it's hard?" about his weird freak genius brain in that he doesn't realized quite how much of an outlier he is.

Like it seems from Jayce and Viktor's chalkboards and also the scenes of Ekko, AU Powder and Heimerdinger building the Z drive that there is actual rune math involved, in that runes have mathematical properties and you can do equations with them. And I think it's highly unlikely anyone in Piltover formally teaches this branch of mathematics because no one believes magic can be accessed in this way, and also it's not like Jayce is gonna be requesting an elective to learn the stuff needed for his illegal science project. So I'm guessing Jayce was teaching himself an entirely new branch of mathematics probably out of some weird old books imported through slightly irregular means, on top of all his regular coursework/research. Hell, he was probably inventing/discovering new rune math in the process of creating Hextech; by the time the Hexgates are open he could probably write the textbook on it.

With Viktor, I actually think the element he would think was no big deal is his engineering skill. Zaun is absolutely full of crazy tinkerers building shit out of nothing and jerry-rigging solutions to problems and keeping things working with spit, rubber bands and ingenuity. They have advanced prosthetics and body mods (I am sure Viktor's back brace is an Undercity creation; no one in Piltover knows how to make that stuff because no one needs it); they have "potions" that heal serious wounds quickly; even the Firelights' hoverboards are a technology we don't see in Piltover. Jinx and Ekko both figure out how to make usable Hextech artifacts with way fewer resources than anyone in Piltover has; Ekko and AU Powder invent fucking time travel when they have a bit of time to mess around with things.

And when it comes to book learning I'm guessing Viktor had no one to compare himself with as a child, so he's teaching himself calculus at age ten out of a book he stole out of some rich Piltie kid's backpack and thinking this is probably how everyone learns topside. He probably ran circles around his fellow Academy students when it came to formal classwork but he barely pays attention to that because it's not discovery; it's just demonstrating that you know the material and he already knows that he knows it. He spends one evening reading Jayce's notebook and is able to understand enough to know the science is solid and contribute to advancing it. (And how much do I love the idea that he fell for Jayce's brain, as seen through his research notes, before any other part of him.) Viktor builds what's essentially a magical AI (the Hexcore) which no one even knew could be done and is still frustrated that he's not figuring out how it works fast enough.

Tl;dr these guys match each other's freak on a brain level instantly and like no one else around them and that would already be some soulmate-level shit no matter what else you think is going on.

[jcmarchi]

Inside FunSearch: Google DeepMind’s LLM that Discovered New Math and Computer Science Algorithms

New Post has been published on https://thedigitalinsider.com/inside-funsearch-google-deepminds-llm-that-discovered-new-math-and-computer-science-algorithms/

Inside FunSearch: Google DeepMind’s LLM that Discovered New Math and Computer Science Algorithms

Discovering new science is one of the ultimate frontiers for AI.

Created Using DALL-E

In this issue:

An anaysis of Google DeepMind’s FunSearch, a model that was able to discover new algorithms in computer science and mathematics.

Discovering new science might be most complete Turing Test for the AI models. New scientific methods require complex reasoning skills, combining knowledge from many fields, constant experimentation and evaluation, and many other complex cognitive skills. Google DeepMind has been one of the AI labs pushing the frontiers of using AI to streamline our path to new scientific discoveries. Models such as AlphaGo has enabled the discovery of new proteins while AlphaTensor was able to improve classic matrix multiplication algorithms. Google DeepMind’s newest iteration in this area is FunSearch, a model that was able to create new mathematics and computer science algorithms.

FunSearch provides a clever approach to discover new algorithms by “thinking in code”. Essentially, FunSearch uses an LLM to generate computer programs based on a set of functions for a given problem and then uses an evaluator to prove the different solutions. The FunSearch named is derived from the fact that the model iteratively searches the function space.

Inside FunSearch

[orteil42]

Do you consider Mathematics to be an invention or a discovery?

🛑⛔️🚫 "is white a color"/"are video games art"-type semantics squabbling. do not engage do not waste brain cycles on and if possible do not even acknowledge

[goodstuffhappenedtoday]

Louisiana students who solved the Pythagorean theorem discover nine more solutions to it

Two New Orleans students who solved the Pythagorean theorem using trigonometry have had their discovery confirmed by the math community after their findings were published in the American Mathematical Monthly this week, solidifying their proofs. And if solving Pythagoras' theorem wasn't challenging enough, the young women, now college freshmen, also discovered nine more solutions to the problem. Ne'Kiya Jackson and Calcea Johnson, former St. Mary's Academy students, presented their discovery to the American Mathematical Society in Atlanta back in March of 2023. This October, their solutions were peer-reviewed and thoroughly investigated to confirm what many in the math community never could have imagined — the theorem could be solved by using trigonometry.  Many papers submitted to the mathematics journal are often turned down. But after careful consideration and scrutiny, Jackson and Johnson's paper was approved for publication. Jackson and Johnson found the first proof to the equation during their senior year of high school while working tirelessly over their holiday break to solve a bonus question in a math contest. Once deemed impossible, the two students overcame a failure of logic referred to as circular reasoning. But, in their new study, Johnson and Jackson went even further, providing nine other proofs, or solutions to the theorem.  Since the foundation of trigonometry relies on the fact that the Pythagorean Theorem is true, the mathematics community believed using trigonometry to prove the theorem would be unworkable. But it wasn't.  ... Their findings are testament to the idea that dedication pays off.

More at the link